I'm familiar enough with common practice harmony, its rules and methods for diatonically harmonizing the scale, tonicizing scale degrees and modulating into new keys. But these tools seem to lose their relevance when applied to songs that use frequent modulation, modal mixture, non-functional progressions, parallel harmony, etc. Is there a theoretical system for making sense of music that falls outside the realm of common practice rules, which seem incredibly limited by comparison? Or is it open territory at this point, and "if it sounds good, it is good"? I'm talking mainly about jazz and blues, and pop music which uses the ideas in each.

Although I appreciate the more philosophical responses I've gotten so far, I'm really looking for a book that will help me analyze jazz changes in a helpful way; either from a pragmatic standpoint of best practices ("you can add in a ii-V-I and it just works"), or something more theoretically substantial and meaningful.
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Duncan MalashockDec 10 '13 at 23:35

4 Answers
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For jazz there is a lot of theory to embrace. A good source is 'The Jazz Theory Book' by Mark Levine that will guide you through everything and all different styles of jazz. With the knowledge from it you should be able to analyze any jazz song.

With regard to the jazz examples, there really is a theory. It may not have been studied by musicologists at the start or taught in college classes, but it was there, and was picked up and understood by the musicians. In this case when I say "theory" I mean a mental model that has both explanatory and predictive power.

It is easy to see that there is a common theory or mental model that the jazz musicians all know. Take four jazz players who have never met before, let's say a pianist, a guitarist, a trumpet player and a trombone player. Name a tune and see what happens. The pianist and guitarist will start playing the changes and will quickly be in agreement about the ninth chords and eleventh chords. One of the melody instruments will improvise on the tune with the other filling in countermelodies. The sounds will all fit together. That's the predictive power of the theory: improvising is predicting a direction to go in that will work. (Sometimes you get someone who just doesn't understand the style and ruins the whole thing, and everybody knows it.)

These days there are books and college courses about the music of Miles Davis, so you can study it in a more theoretical way, but you can probably best understand it by playing it with good musicians.

Blues and the different kinds of rock and pop music each have their own styles. Unfortunately there isn't a "Grand Theory of Everything" that works for all music. There are some examples of music that can be looked at in two different theoretical frameworks such as jazz and French Impressionism, perhaps with different results.

Ok, I think that's a valid response, but I already play music; I'm looking for something to help me understand jazz harmony in a more meaningful way, so I'm not just going by what sounds good. Can you help?
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Duncan MalashockDec 10 '13 at 23:39

Indeed, common practice tonal analysis really begins to break down around the turn of the century. One of the problems theorists, composers, and musicians are encountering today is that the horizon is now so wide, there is no single zeitgeist through which musicians operate. This is unique because it has never occurred throughout music history before the 20th century.

That said, there are some analytical frameworks that have cropped up in an attempt at explaining some of what has been going on:

Set Theory

12-Tone Composition

Serialism

Schenkerian Analysis

These are a few of the major avenues. The rest of typical contemporary techniques fall under an incredibly large umbrella of "isms": Dadaism, Fluxism, Modernism, Post-Modernism, Expressionism, Primitivism, Neo-Classicism, Neo-Romanticism, etc etc. Each of these "genres" contains specific techniques or modes of thought / aesthetic that informs the art, and thereby analysis.

What is most astounding is that the above essentially only covers acoustic music, and does not allow for musique concète, acousmatic, electronic, mixed media, interactive or performance art.

Currently, almost every piece of music is entirely situational, each with its own series of rules, architecture, and anatomy.

Each time someone "figures out" a new concept, it becomes less interesting...
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aweDec 10 '13 at 7:47

Maybe my question is too broad or vague. I appreciate your knowledge of the classifications, and that no one's got all the answers, but is there somewhere you recommend I can start, at least in terms of jazz harmony and how to explain it in terms of songwriting strategies?
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Duncan MalashockDec 10 '13 at 23:42

Short of enrolling in a Jazz Harmony / Theory / Arranging class, I'd recommend purchasing either a Real Book or a Fake Book and study all the charts. Jazz is a language that developed out of common practice techniques, so you'll always see traces of that in the music. Really the largest differences are upper-tertian harmony and extended chromaticism. Also, I would make sure you understand what "type" of jazz you are studying. For example, free jazz, smooth jazz, and bebop jazz all have different rules / characteristics that are specific to their harmonic and melodic material.
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jjmusicnotesDec 11 '13 at 4:17

That's helpful, but I want to make a distinction here between stylistic characteristics and an analytical system. Maybe hard bop jazz has particular characteristics in terms of how the music is classified, but that's not the same as describing techniques and rules which describe the options and strategies for composition.
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Duncan MalashockDec 18 '13 at 21:06

For me it's the opposite: common practice harmony makes even apparently complex jazz progressions seem easy, and 90 per cent of times I am able to use common practice harmony 'rules' to any popular music progression. Not a bad feat, if you ask me. I'd say it depends on how deep is your knowledge of common practice harmony, often one thinks they 'know' it when all they did was reading about rules but rarely practicing all this useful stuff in a concrete way. I am not saying that's your case, I am speaking in general. Having said that, it makes sense to learn harmony from the jazz point of view, i.e. study jazz harmony.